Blog and Podcast for all enthusiastic Theory of Knowledge (TOK) students and teachers (and anybody else!)as a source of inspiration. TOK is an epistemology and critical thinking course offered by the International Baccalautreate (IB) Organization. It's a course in practical and applied philosophy.

It is not always necessary to conduct real-life experiments to reach a valid scientific conclusion. Thought experiments may in some cases also suffice. In this edition I will illustrate you a thought experiment from physics: In a vacuum, all objects accelerate the same way and they both have the same velocity. Heavy objects will not fall faster. But how can we test this? We do not have a large vacuum chamber to test this. A thought experiment can be useful in this case.

In this edition of TOK-Talk I will explain you what a thought experiment is. Is it always necessary to conduct real-life experimets to reach a valid scientific conclusion? Listen to find out!
Do heavy or lighter objects fall to the ground faster? Which one will hit the ground first when dropped at the same time from the same height – a bowling ball or a ball of crumpled newspaper of the same size? The answer is: “it depends”! If you drop both objects from a tower on earth, then the bowling ball will hit the ground first. If you drop both objects on the moon, then both will hit the ground at the same time. Here on earth, the air resistance has a large influence on the falling velocity of an object. In a complete vacuum all objects hit the the ground at the same time. This may be difficult to imagine, but it is indeed the case.

The problem is that we can not go to the moon to test this physical law. We could construct a giant air-less vacuum chamber here on earth. But this is of course not practical – and not necessary either! I would like to introduce to you a thought experiment that demonstrates that all objects do indeed fall to the ground at the same rate. Now, it is very critical that we take the experiment step by step, otherwise it can become a bit confusing.

Step 1: We start the thought experiment by making an assumption. We assume that heavy objects fall to the gound faster than light objects. I know that I just told you that in a vacuum all objects fall to the ground at the same rate, but for right now we need to take this assumption. Again: we assume that heavy objects fall to the ground faster. I take a square block of lead with a mass of 10kg into my left hand and a block of lead with a mass of only 1kg into my right hand. Actually you have to be pretty strong to carry the 10kg lead block in one hand, but as we do this only in our imagination, this is not a problem. I drop them both at the same time from the same height. The 10kg lead block will hit the ground before the 1kg block. It will accelerate faster. We hear two sounds as the two blocks hit the floor: boom – boom. The first boom is from the 10kg block and the second boom is from the 1kg block hitting the floor. This is what we assume. Close your eyes and try to imagine this situation. Just don’t drop them on your toes.

Step 2: I now pick up both blocks of lead from the floor. Luckily it is only a thought experiment so no real damage has been done to the floor (or your toes). In your imagination put the larger 10kg block of lead on top of the 1kg block. The two blocks are now stacked on top of each other. You now have one chunk of lead, 11kg heavy. The large block is sitting on the small one. The next observation is crucial. Drop this chunk from the same height. What should happen? The smaller block will fall slower than the larger one. The larger block wants to fall faster, but is slowed down by the smaller block in front of it. The falling velocity of the 11kg combination block will therefore be between the velocity of the 10kg and the 1kg block when they are dropped separately. The combination block will fall slower than the 10kg block alone. This is because the small block breaks the falling of the larger block behind it. Actually the situation is similar to two people running, a fast person running behind a slow person. The fast runner bumps into the slower runner in front. The faster runner is slowed down.

Step 3: Now it’s starting to become interesting. Remember our assumption from the beginning? We assumed that heavier objects fall to the ground faster than lighter objects. But is this not strange? If this assumption is correct then the 11kg combination block should actually fall faster than the 10kg block alone. But as we have just seen, we came to the conclusion that the combination block falls slower. Our conclusion contradicts the initial assumption. Something is wrong here. But what?

The assumption is wrong. If we assume that all objects fall to the ground (in a vacuum of course) at the same rate, then we do not have this contradiction. It then does not matter if the block of lead has a mass of 1kg, 10kg or 11kg. All of them fall to the ground at the same rate. And indeed, this is what we observe in space. If we reach contradictory conclusions, then either we made a mistake in the deductive process or the assumptions are wrong. But we made no errors, so the assumption must be wrong.

This method of trying to contradicting the assumptions is also used in the field of Mathematics. Certain mathematical proofs are conducted in a similar way. Initially you make a false assumption and then try to disprove this assumption by generating a contradiction.

For those of you who still doubt that all objects fall to the ground the at same rate, I have another explanation. Objects with a larger mass also are pulled by gravity with a stronger force. A heavy shopping bag pulls on our arms with greater force than a light shopping bag. That’s why our arms start to hurt faster. So far so good. But does this mean that a heavy shopping bag also falls faster to the ground? Objects that have a larger mass are also more difficult to accelerate. In simple words, heavy objects don’t like to move from their place when you apply a force to them. This is why heavier cars need stronger engines to accelerate them. Otherwise you’ll get off the spot only very slowly. Now, this larger mass compensates the stronger pulling force. Example: a bowling ball is pulled to the ground more than a golf ball. But the bowling ball also wants to resist the movement more than the golf ball. The consequence is that both objects fall to the gound at the same rate again. Golf ball and bowling ball will contact the ground at the same time.

After so much imagination work a little final quote by Galileo Galilei: “All truths are easy to understand once they are discovered; the point is to discover them.”